This example breaks regular language, because number of each element
is critical. This prevents pumping (no way to construct larger
strings using a single repeated substring) , and thus you would need
an arbitrarily large FA.

Connection between stacks and CFGs - the addition of the stack to a
FA results makes a pushdown automata. The infinite stack allows
a the acceptance of a context free languages (such as the example
above) by pushdown automatas which cannot be accepted by FAs.